A city gas contains unsaturated hydrocarbon C2.73H4.72
(8.4 percent), saturated hydrocarbon C1.14H4.28 (10.1
percent), hydrogen (39.9 percent), carbon monoxide (32.9 percent), carbon
dioxide (2.6 percent), nitrogen (5.4 percent) and oxygen (0.7 percent). Calculate heating value of this gas. Heating values for saturated and unsaturated
hydrocarbons could be obtained using the empirical relationships:
For unsaturated hydrocarbons (CmHn) =
98,200m plus 28,200n plus 28,800 calories per mol. In this relationship, m denotes number of carbon atoms, and n,
number of hydrogen atoms.
For saturated hydrocarbons (CmHn) =
158,100n plus 54,700 calories per mol.
Solution:
Let’s consider one mole of this gas as a basis of
calculations.
For Unsaturated hydrocarbon, using m = 2.73 and n =
4.72. Heating value is calculated as
429,990 calories per mole. This
component is present in the amount of 8.4 percent, or 0.084 mole. Thus the contribution of unsaturated
hydrocarbon in the heating value of the city gas is 0.084 times 429,990 =
36,120 calories.
For saturated hydrocarbon, using m = 1.14 n = 4.28. Heating value is calculated as 234,934
calories per mole. This component is
present in the amount of 0.0101 mole.
Its contribution is 0.0101 times 429,990 = 36,120 calories.
Heating value of hydrogen can be obtained from any reference
book. Note that heating value of a
compound is heat obtained when that compound is burnt completely. Its value is same as the negative of heat of
formation. Thus, for hydrogen, heating
value is 68,317 calories per mole. As
hydrogen is 0.399 mole, its contribution is 0.399 times 68,317 = 27,259
calories.
For carbon monoxide, heating value is 67,636 calories per
mole. Its contribution is 22,252
calories.
Heating value of the city gas can now be calculated by
adding the contribution of all components and is found to be 109,359 calories
per mole or 196,840 BTUs per pound mole.
Note that one calorie per gram mole is 1.8 BTU per pound mole. Heating value = 196,840 divided by 385.2 =
511 BTU per dry standard cubic foot completely saturated.
Let’s give the details of this magic number 385.2.
An ideal gas occupies 359.05 cubic feet at 1 atmosphere and
32 degrees Fahrenheit. It is an
established industrial practice that gas measurement is done at pressure of 30
inches of mercury and a temperature of 60 degrees Fahrenheit. Specific volume of gas at these conditions
is 378.48 cubic feet.
Vapor pressure of water at 60 degrees F is 0.52”
mercury. Thus, mole fraction of the dry
gas is can be calculated as 0.9827. Specific volume of gas that is completely
saturated = 378.48 divided by 0.9827 = 385.16 cubic feet.